2010-11: Kasperi Kapanen played for KalPa Kuopio's U16 team as a 14-year-old and attended the Pohjola Camp for the top young players in Finland. He scored 14 goals with 8 assists and had 10 penalty minutes in 26 U16 games.
2011-12: Kapanen scored at nearly a point-per-game pace for KalPa's U18 team and was among the leading scorers for Finland's U16 team. He scored 13 goals with 11 assists and had 6 penalty minutes in 27 games, including two playoff contests, for the Kuopio club. Kapanen and KalPa teammate Miikka Pitkanen scored 11 goals each to lead Finland's U16 team and Kapanen had 6 assists; finishing +11 with 20 penalty minutes in 13 international games. Skating for Finland in the 2011 Europe Youth Olympic Games tournament he scored 4 goals with 2 assists and was +3 with 2 penalty minutes in six games.
2012-13: Kapanen made his SM-Liiga debut in December 2012 — joining his father, former NHLer Sami Kapanen, in the KalPa Kuopio lineup —and was one of the top scorers for KalPa's junior team. He represented Finland in three international tournaments, the 2012 U18 Ivan Hlinka Memorial Tournament in August, the 2013 U18 World Junior Championship, and the 2013 U17 World Hockey Challenge in Canada. Kapanen scored 4 goals and was +1 with 2 penalty minutes; averaging 11 minutes of ice time in 13 regular season SM-Liiga games. In four playoff games he had 1 assist and was +1 with 2 penalty minutes. He played 36 games for the KalPa U20 team, scoring 14 goals with 15 assists, and was -3 with 16 penalty minutes. Kapanen played 13 games for Finland in the two U18 tournaments, scoring 9 goals with 5 assists, and was +7 with 6 penalty minutes. In five games at the WHC he scored 3 goals with 6 assists and had 4 penalty minutes.
2013-14: Kapanen assumed a full-time spot with KalPa as a 17-year-old after scoring 3 goals and accumulating 16 penalty minutes in six games during the summer European Trophy tournament.